Quantum phase transitions (QPT) were investigated to show that the Hertz φ4 theory of quantum criticality is incomplete as it misses anomalous nonlocal contributions to the interaction vertices. The theory was found to be renormalizable for antiferromagnetic quantum transitions only if the dynamical exponent z=2. The Gaussian fixed point was found to split into two non-Gaussian fixed points for d<2. The results show that for both fixed points, the dynamical exponent remains z=2.
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We acknowledge stimulating conversations with A. G. Abanov, I. Gruzberg, O. Starykh, and I. Vekhter. The work of Ar. A. was supported by the Oppenheimer Fellowship in Los Alamos. A. Ch. acknowledges support from NSF DMR 0240238. We thank the Aspen Center for Physics for hospitality.